The 1-0 triumph over their city rivals ensured Barca stayed within a point of La Liga leaders Atletico Madrid, and maintained their two-point advantage over third-placed Real Madrid.
A Lionel Messi penalty 13 minutes from time was enough to seal the victory for Gerardo Martino's side, who were regularly frustrated by Espanyol, and Alves said they had expected a tough test.
"It's hard to win here because of who we play against," he said.
"They apply a lot of pressure and they are intense in their approach to the game.
"We knew that it would be difficult, but I thought we played a great first half. We gave it our all.
"We're doing well and we're confident, but we know how hard it's going to be.
"We are ready to fight until the end. We never lost our intensity, our rivals play football too – they are playing for their lives in this competition, it makes it all very difficult.
"Barca may not win all their games comfortably, sometimes we can, other times we cannot."
The victory leaves Barcelona on 75 points from 31 matches, with the Catalan giants having seven games left to try and move above Atletico in the title race - though the duo will face off at Camp Nou on the final day of the season.
